Bayesian Sequential Change Diagnosis

References

• Arrow K. J., Blackwell D., Girshick M. A. Bayes and minimax solutions of sequential decision problems. Econometrica (1949) 17:213–244MR0032173 (11,261h)Crossref, Google Scholar
• Barlow R. E.Engineering Reliability (1998) (Society for Industrial and Applied Mathematics (SIAM), Philadelphia) ASA-SIAM Series on Statistics and Applied ProbabilityMR1621421 (99m:62150)Crossref, Google Scholar
• Basseville M., Nikiforov I. V.Detection of Abrupt Changes: Theory and Application (1993) (Prentice Hall Inc., Englewood Cliffs, NJ) Prentice Hall Information and System Sciences SeriesMR1210954 (95g:62153)Google Scholar
• Bertsekas D. P.Dynamic Programming and Optimal Control (2001) II2nd ed.(Athena Scientific, Belmont, MA) . MR2182753Google Scholar
• Blackwell D., Girshick M. A.Theory of Games and Statistical Decisions (1979) (Dover Publications Inc., New York) . [Reprint of the 1954 edition.] MR597146 (82a:90191)Google Scholar
• Chow Y. S., Robbins H., Siegmund D.Great Expectations: The Theory of Optimal Stopping (1971) (Houghton Mifflin Co., Boston, MA) . MR0331675 (48 10007)Google Scholar
• de Boor C.A Practical Guide to Splines, Applied Mathematical Sciences (2001) 27revised ed.(Springer-Verlag, New York) . MR1900298 (2003f:41001)Google Scholar
• Dragalin V. P., Tartakovsky A. G., Veeravalli V. V. Multihypothesis sequential probability ratio tests. I. Asymptotic optimality. IEEE Trans. Inform. Theory (1999) 45(7):2448–2461MR1725130 (2000k:62144)Crossref, Google Scholar
• Dragalin V. P., Tartakovsky A. G., Veeravalli V. V. Multihypothesis sequential probability ratio tests. II. Accurate asymptotic expansions for the expected sample size. IEEE Trans. Inform. Theory (2000) 46(4):1366–1383MR1768555 (2001d:62077)Crossref, Google Scholar
• Glasserman P.Monte Carlo Methods in Financial Engineering. Applications of Mathematics, Vol. 53. Stochastic Modelling and Applied Probability (2004) (Springer-Verlag, New York) . MR1999614 (2004g:65005)Google Scholar
• Green P. J., Silverman B. W.Nonparametric Regression and Generalized Linear Models. Monographs on Statistics and Applied Probability, Vol. 58. A Roughness Penalty Approach (1994) (Chapman & Hall, London) . MR1270012 (95k:62106)Google Scholar
• Klugman S. A., Panjer H. H., Willmot G. E.Loss Models (1998) (John Wiley & Sons Inc., New York) Wiley Series in Probability and Statistics: Applied Probability and Statistics[From data to decisions, With the assistance of Gary G. Venter, A Wiley-Interscience Publication.] MR1490300 (99b:62155)Google Scholar
• Lai T. L. Sequential multiple hypothesis testing and efficient fault detection-isolation in stochastic systems. IEEE Trans. Inform. Theory (2000) 46(2):595–608Crossref, Google Scholar
• Lai T. L. Sequential analysis: Some classical problems and new challenges. Statist. Sinica (2001) 11(2):303–408[With comments and a rejoinder by the author.] MR1844531 (2002d:62001)Google Scholar
• Longstaff F. A., Schwartz E. S. Valuing American options by simulation: A simple least-squares approach. Rev. Financial Stud. (2001) 14(1):113–147Crossref, Google Scholar
• Nikiforov I. V. A generalized change detection problem. IEEE Trans. Inform. Theory (1995) 41(1):171–187Crossref, Google Scholar
• Ramsay J. O., Silverman B. W.Functional Data Analysis (2005) 2nd ed.(Springer, New York) Springer Series in StatisticsMR2168993Crossref, Google Scholar
• Ross S. M. Stochastic processes. Lectures in Mathematics (1983) 14(John Wiley & Sons Inc., New York) Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical StatisticsMR683455 (84m:60001)Google Scholar
• Shiryaev A. N. Optimal methods in quickest detection problems. Teor. Verojatnost. i Primenen. (1963) 8:26–51MR0155708 (27 5642)Google Scholar
• Shiryaev A. N. Optimal stopping rules. Applications of Mathematics (1978) 8(Springer-Verlag, New York) . [Translated from the Russian by A. B. Aries.] MR0468067 (57 7906)Google Scholar
• Tsitsiklis J. N., Roy V. B. Regression methods for pricing complex American-style options. IEEE Trans. Neural Networks (2001) 12:694–703Crossref, Google Scholar
• Wald A., Wolfowitz J. Bayes solutions of sequential decision problems. Ann. Math. Statist. (1950) 21:82–99MR0034005 (11,529c)Crossref, Google Scholar